<p><b>Abstract</b>—We examine the histogram method proposed in [<ref rid="bibi02161" type="bib">1</ref>] for estimating the parameters associated with a Markov random field. This method relies on the estimation of the local interaction sums from histogram data. We derive an estimator for these quantities that is optimal in a well-defined sense. Furthermore, we show that the final step of the histogram method, the solution of a least-squares problem, can be done substantially faster than one might expect if no equation culling is used. We also examine the use of weighted least-squares and see that this seems to lead to better estimates even with small amounts of data.</p>